Online program [1]
- Magnetic symmetry identification [1, 2]
- Determination of oriented spin space groups [3]
- Emergent physics
- Symmetry analysis of magnetic phases [3], spin splitting [1], quantum transport [4], and beyond.
- Disentanglement of magnetic geometry and spin-orbit coupling effects [2, 3].
Spin Space Group Database [1]
- Search spin space group by Chen-Liu nomenclature [1, 2]
- Generators and general positions of spin space groups [2]
- Wyckoff positions and site symmetry groups of spin space groups [2]
Data Resources
Supplementary Resources- Collinear spin space group-symmetry General positions, Wyckoff positions, spin site symmetry groups, spin Brillouin zones, little co-groups of wavevectors, band representations. Ref [5]
- Tables of altermagnets All altermagnets and corresponding momentum position of altermagnetic spin splitting in MAGNDATA. Ref [5]
- Candidate materials exhibiting unconventional magnons Magnon band structures of collinear magnets and corresponding band representations. Ref [5]
- Tables of nontrivial Spin Space Group Enumerated spin space groups data are provided. Ref [2]
- Identified Materials in MAGNDATA All experimentally determined magnetic structures in the MAGNDATA database. Ref [2]
- Second-order transport tensors of antiferromagnets A database of AFMs with second-order conductivity tensors allowed by SSG symmetry. Ref [2, 4]
- Character tables of corepresentations of double spin point groups (beta) Character tables of corepresentations of double spin point groups.
References
Publications[1] Y. Yu, X. Chen*, Y. Zhu, Y. Li, R. Xiong, J. Li, Y. Liu and Q. Liu*. Identifying Oriented Spin Space Groups and Related Physical Properties Using an Online Platform FINDSPINGROUP. arXiv (2026). arXiv:2604.21397
[2] X. Chen†, J. Ren†, Y. Zhu†, Y. Yu†, A. Zhang, P. Liu, J. Li, Y. Liu, C. Li and Q. Liu*. Enumeration and representation theory of spin space groups. Phys. Rev. X 14, 031038 (2024). doi:10.1103/PhysRevX.14.031038
[3] Y. Liu†, X. Chen†, Y. Yu, J. Etxebarria, J. M. Perez-Mato and Q. Liu*. Symmetry classification of magnetic orders using oriented spin space groups. Nature 652, 869-873 (2026). doi:10.1038/s41586-026-10401-1
[4] H. Zhu†, J. Li†, X. Chen, Y. Yu and Q. Liu*. Magnetic geometry induced quantum geometry and nonlinear transports. Nat. Commun. 16, 4882 (2025). doi:10.1038/s41467-025-60128-2
[5] X. Chen, Y. Liu, P. Liu, Y. Yu, J. Ren, J. Li, A. Zhang and Q. Liu*. Unconventional magnons in collinear magnets dictated by spin space groups. Nature 640, 349-354 (2025). doi:10.1038/s41586-025-08715-7
[6] P. Liu, J. Li, J. Han, X. Wan* and Q. Liu*. Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling. Phys. Rev. X 12, 021016 (2022). doi:10.1103/PhysRevX.12.021016
[7] Y. Li†, S. Zeng†, X. Chen†, R. Xiong, Y. Yu, Y.-J. Zhao and Q. Liu*. Symmetry-guided prediction of magnetic-ordered ground states. arXiv (2025). arXiv:2512.21672
